Bruno Genesio's side extended their unbeaten run to six matches to drop Monaco down a spot into third ahead of this weekend's clash at Lille, while their opponents remain just four points above the relegation zone.
The away side began to dominate from kick-off and Alexandre Lacazette collected Sergi Darder's cross before forcing goalkeeper Geoffrey Jourdren into a save in the opening exchanges.
At the other end Jamel Saihi had a shot blocked before team-mate Mustapha Yatabare's effort on target was held, but it was the visitors who took the lead just after the half-hour mark through Cornet.
Jordan Ferri provided the assist for the 19-year-old striker, who fired a shot into the bottom corner.
And he doubled his tally five minutes before the break after picking up Lacazette's throughball and shooting home from close range for his seventh goal this season.
Lacazette was caught offside eight minutes after the break when put through by Maxime Gonalons and the France striker came close again by sending Rachid Ghezzal's cross wide of the mark and was also off target after being set up by Henri Bedimo.
The hosts came close to pulling one back as Jonas Martin picked out Souleymane Camara, but the Senegal international fired wide.
Mathieu Valbuena had two good chances in quick succession at the death, but failed to add to Les Gones' total.